# Factors of 217

Factors of 217 are 1, 7, 31, and 217

#### How to find factors of a number

 1.   Find factors of 217 using Division Method 2.   Find factors of 217 using Prime Factorization 3.   Find factors of 217 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 217

• Divide 217 by 1: 217 ÷ 1 : Remainder = 0
• Divide 217 by 7: 217 ÷ 7 : Remainder = 0
• Divide 217 by 31: 217 ÷ 31 : Remainder = 0
• Divide 217 by 217: 217 ÷ 217 : Remainder = 0

Hence, Factors of 217 are 1, 7, 31, and 217

#### 2. Steps to find factors of 217 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 217 using the division method, follow these steps:

• Step 1. Start dividing 217 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 217, which is 7. Divide 217 by 7 to obtain the quotient (31).
217 ÷ 7 = 31
• Step 3. Repeat step 1 with the obtained quotient (31).
31 ÷ 31 = 1

So, the prime factorization of 217 is, 217 = 7 x 31.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 217 as shown below:

So, the prime factorization of 217 is, 217 = 7 x 31.

#### 3. Find factors of 217 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 217 would be the two numbers which, when multiplied, give 217 as the result.

The following table represents the calculation of factors of 217 in pairs:

Factor Pair Pair Factorization
1 and 217 1 x 217 = 217
7 and 31 7 x 31 = 217

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 217. They are called negative pair factors.

Hence, the negative pairs of 217 would be ( -1 , -217 ) , ( -7 , -31 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 7, 31, 217 are exact divisors of 217.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 217 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 217.

• What are the prime factors of 217?

The factors of 217 are 1, 7, 31, 217.
Prime factors of 217 are 7, 31.

• What is the sum of all factors of 217?

The sum of all factors of 217 is 256.

• What are the pair factors of 217?

Pair factors of 217 are (1,217), (7,31).

• What two numbers make 217?

Two numbers that make 217 are 7 and 31.

• What are multiples of 217?

First five multiples of 217 are 434, 651, 868, 1085.

• Is 217 a perfect square?

No 217 is not a perfect square.

• Which is greatest factor of 217?

The greatest factor of 217 is 31.

• How do you factors of 217?

Factors of 217 are 1, 7, 31, 217.

• What are five multiples of 217?

First five multiples of 217 are 434, 651, 868, 1085, 1302.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 217?

Factors of 217 are 1, 7, 31, 217.
Even factors of 217 are 0.
Hence, product of even factors of 217 is; 0 = 0.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 217? Help her in writing all the factors.

Positive factors are 1, 7, 31, 217.
Negative factors are -1, -7, -31, -217.

How many factors are there for 217?

Factors of 217 are 1, 7, 31, 217.
So there are in total 4 factors.

Sammy is puzzled while calculating the prime factors of 217. Can you help him find them?

Factors of 217 are 1, 7, 31, 217.
Prime factors of 217 are 7, 31

Joey wants to write all the prime factors of 217 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 217 are 7, 31.
So in exponential form it can be written as 7 x 31.

What is prime factorization of 217?

Prime factorization of 217 is 7 x 31 = 7 x 31.

Can you help Rubel to find out the product of the even factors of 217?

Factors of 217 are 1, 7, 31, 217.
Even factors of 217 are 0.
Hence, product of even factors of 217 is; 0 = 0.